The elliptic sinh-Gordon equation in a semi-strip
We study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems. Based on the spectral analysis for the Lax pair formulation, we show that the spectral functions can be character...
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-06-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2016-0206 |
| Summary: | We study the elliptic sinh-Gordon equation posed in a
semi-strip by applying the so-called Fokas method, a
generalization of the inverse scattering transform for boundary
value problems. Based on the spectral analysis for the Lax pair
formulation, we show that the spectral functions can be
characterized from the boundary values.
We express the solution of the equation
in terms of the unique solution of the matrix Riemann–Hilbert problem
whose jump matrices are defined by the
spectral functions. Moreover, we
derive the global algebraic relation that involves the boundary
values. In addition, it can be verified that the solution of the
elliptic sinh-Gordon equation posed in the semi-strip exists if
the spectral functions defined by the boundary values satisfy this
global relation. |
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| ISSN: | 2191-9496 2191-950X |